Because people feel several things on the topic. Top reasons I have heard -

- Docs are already gearing toward "specialists" which is making the General Practitioners as glorified Nurses who write you a prescription to said specialist. With the idea of "free" health care creates the fear that the best Docs will go to a place where they can name their price rather than being compensated what the federal government feels like compensating them.

- The idea that you go on a "first come, first served" allows the opportunities for those who aren't "bleeding" to potentially die (this is no joke, people think this) because they don't "appear" to be as critical as say a car crash victim who is in a stable condition, but still in need of stitches. Brock Lesner actually talked about something similar to this when dealing with his illness in Canada. He felt that had he not returned to the States when he did, he would not have survived his illness due to it being severe, yet the Docs treated him as a "non-critical" patient.

- The idea scares most people. Government controlling you doctors, the idea that hypochondriacs who go to the doctor when they cough stock piling the ER, the aspect of the government supporting programs they don't agree with (Planned Parenthood with abortions for example)... These ideas frighten people that the "Free Health Care" program presented is not one that they would agree with for numerous reason creates a fear that "Big Brother" is trying to control the masses. Sadly, this is just fueled by the fan of Mass Media outlets fanning the flames with their hot air being spewed.